Browsing by Subject "particle filter"

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    A sequential Monte Carlo Gibbs coupled with stochastically approximated expectation-maximization algorithm for functional data
    (International Press, 2022-01-11) Liu, Ziyue; Biostatistics and Health Data Science, School of Medicine
    We develop an algorithm to overcome the curse of dimensionality in sequential Monte Carlo (SMC) for functional data. In the inner iterations of the algorithm for given parameter values, the conditional SMC is extended to obtain draws of the underlying state vectors. These draws in turn are used in the outer iterations to update the parameter values in the framework of stochastically approximated expectation-maximization to obtain maximum likelihood estimates of the parameters. Standard errors of the parameters are calculated using a stochastic approximation of Louis formula. Three numeric examples are used for illustration. They show that although the computational burden remains high, the algorithm produces reasonable results without exponentially increasing the particle numbers.
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    A Particle Filter Approach to Multiprocess Dynamic Models with Application to Hormone Data
    (Springer, 2015-10) Liu, Ziyue; Department of Biostatistics, Richard M. Fairbanks School of Public Health
    We extend the multiprocess dynamic models to the general non-Gaussian and nonlinear setting. Under this framework, we propose specific models to simultaneously model hormone smooth basal trend and pulsatile activities. The pulse input is modeled by two processes: one as a point mass at zero and one as a gamma distributed random variable. This gamma-driven approach ensures the pulse estimates to be nonnegative, which is an intrinsic characteristic of hormone dynamics. The smooth trend is modeled by smoothing splines. Both additive and multiplicative observational errors are investigated. Parameters are estimated by maximizing the marginal likelihood. Baseline and pulses are estimated by posterior means. For implementation, particle filter is adopted. Unlike the traditional condensation method where a single distribution is used to approximate a mixture of distributions, this particle filter approach allows the model components to be accurately evaluated at the expense of computational resources. The specific models are applied to a cortisol series. The finite sample performance is evaluated by a simulation. The data application and the simulation show that the biological characteristics can be incorporated and be accurately estimated under the proposed framework.